WKB-Expansion of the HarishChandra-Itzykson-Zuber Integral for Arbitrary β(Condensed Matter and Statistical Physics)

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概要

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• This article is devoted to the asymptotic expansion of the generalized HarishChandra-Itzykson-Zuber matrix integral for non-unitary symmetries characterized by a parameter β (as usual, the values β=1, 2 and 4 correspond to the orthogonal, unitary and symplectic group integrals). The results are of the form [numerical formula], in which χ_i and λ_i are the eigenvalues of the two k×k matrices, and [numerical formula]. A WKB-expansion of f is derived from the heat kernel differential equation for general values of k and β. From an expansion in terms of zonal polynomials, one obtains an expansion in powers of the T_<ij> for β=1, and generalizations are considered for general β. A duality relation, as well as a transformation of products of pairs of symmetric functions into polynomials in the T_<ij>, is used to obtain the expression for f(T_<ij>) for general β.

• 理論物理学刊行会の論文
• 2006-09-25

著者

• HIKAMI Shinobu

  Department of Pure and Applied Sciences, University of Tokyo

• Hikami Shinobu

  Department Of Basic Sciences University Of Tokyo

• BREZIN Edouard

  Laboratoire de Physique Theorique, Ecole Normale Superieure

• Brezin Edouard

  Laboratoire De Physique Theorique Ecole Normale Superieure

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